Patrick L Purdon

Harvard Medical School, Boston, Massachusetts, United States

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Publications (80)308.8 Total impact

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    ABSTRACT: Combining electroencephalogram (EEG) recording and functional magnetic resonance imaging (fMRI) offers the potential for imaging brain activity with high spatial and temporal resolution. This potential remains limited by the significant ballistocardiogram (BCG) artifacts induced in the EEG by cardiac pulsation-related head movement within the magnetic field. We model the BCG artifact using a harmonic basis, pose the artifact removal problem as a local harmonic regression analysis, and develop an efficient maximum likelihood algorithm to estimate and remove BCG artifacts. Our analysis paradigm accounts for time-frequency overlap between the BCG artifacts and neurophysiologic EEG signals, and tracks the spatiotemporal variations in both the artifact and the signal. We evaluate performance on: simulated oscillatory and evoked responses constructed with realistic artifacts; actual anesthesia-induced oscillatory recordings; and actual visual evoked potential recordings. In each case, the local harmonic regression analysis effectively removes the BCG artifacts, and recovers the neurophysiologic EEG signals. We further show that our algorithm outperforms commonly used reference-based and component analysis techniques, particularly in low SNR conditions, the presence of significant time-frequency overlap between the artifact and the signal, and/or large spatiotemporal variations in the BCG. Because our algorithm does not require reference signals and has low computational complexity, it offers a practical tool for removing BCG artifacts from EEG data recorded in combination with fMRI. Copyright © 2015. Published by Elsevier Inc.
    NeuroImage 07/2015; DOI:10.1016/j.neuroimage.2015.06.088
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    ABSTRACT: Anaesthetic drugs act at sites within the brain that undergo profound changes during typical ageing. We postulated that anaesthesia-induced brain dynamics observed in the EEG change with age. We analysed the EEG in 155 patients aged 18-90 yr who received propofol (n=60) or sevoflurane (n=95) as the primary anaesthetic. The EEG spectrum and coherence were estimated throughout a 2 min period of stable anaesthetic maintenance. Age-related effects were characterized by analysing power and coherence as a function of age using linear regression and by comparing the power spectrum and coherence in young (18- to 38-yr-old) and elderly (70- to 90-yr-old) patients. Power across all frequency bands decreased significantly with age for both propofol and sevoflurane; elderly patients showed EEG oscillations ∼2- to 3-fold smaller in amplitude than younger adults. The qualitative form of the EEG appeared similar regardless of age, showing prominent alpha (8-12 Hz) and slow (0.1-1 Hz) oscillations. However, alpha band dynamics showed specific age-related changes. In elderly compared with young patients, alpha power decreased more than slow power, and alpha coherence and peak frequency were significantly lower. Older patients were more likely to experience burst suppression. These profound age-related changes in the EEG are consistent with known neurobiological and neuroanatomical changes that occur during typical ageing. Commercial EEG-based depth-of-anaesthesia indices do not account for age and are therefore likely to be inaccurate in elderly patients. In contrast, monitoring the unprocessed EEG and its spectrogram can account for age and individual patient characteristics. © The Author 2015. Published by Oxford University Press on behalf of the British Journal of Anaesthesia. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
    BJA British Journal of Anaesthesia 07/2015; 115 Suppl 1:i46-i57. DOI:10.1093/bja/aev213
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    ABSTRACT: Little is known about ageing-related changes in the brain that affect emergence from general anaesthesia. We used young adult and aged Fischer 344 rats to test the hypothesis that ageing delays emergence from general anaesthesia by increasing anaesthetic sensitivity in the brain. Time to emergence was determined for isoflurane (1.5 vol% for 45 min) and propofol (8 mg kg(-1) i.v.). The dose of isoflurane required to maintain loss of righting (LOR) was established in young adult and aged rats. The efficacy of methylphenidate to reverse LOR from general anaesthesia was tested. Separate young adult and aged rats with implanted electroencephalogram (EEG) electrodes were used to test whether ageing increases sensitivity to anaesthetic-induced burst suppression. Mean time to emergence from isoflurane anaesthesia was 47 s [95% CI 33, 60; young adult) compared with 243 s (95% CI 185, 308; aged). For propofol, mean time to emergence was 13.1 min (95% CI 11.9, 14.0; young adult) compared with 23.1 min (95% CI 18.8, 27.9; aged). These differences were statistically significant. When methylphenidate was administered after propofol, the mean time to emergence decreased to 6.6 min (95% CI 5.9, 7.1; young adult) and 10.2 min (95% CI 7.9, 12.3; aged). These reductions were statistically significant. Methylphenidate restored righting in all rats during continuous isoflurane anaesthesia. Aged rats had lower EEG power and were more sensitive to anaesthetic-induced burst suppression. Ageing delays emergence from general anaesthesia. This is due, at least in part, to increased anaesthetic sensitivity in the brain. Further studies are warranted to establish the underlying causes. © The Author 2015. Published by Oxford University Press on behalf of the British Journal of Anaesthesia. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
    BJA British Journal of Anaesthesia 07/2015; 115 Suppl 1:i58-i65. DOI:10.1093/bja/aev112
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    ABSTRACT: Electroencephalogram (EEG) approaches may provide important information about developmental changes in brain-state dynamics during general anesthesia. We used multi-electrode EEG, analyzed with multitaper-spectral methods and video recording of body movement to characterize the spatiotemporal dynamics of brain activity in 36 infants 0-6 months old when awake, and during maintenance-of and emergence-from sevoflurane general anesthesia. During maintenance: 1)slow-delta oscillations were present in all ages; 2)theta and alpha oscillations emerged around 4months; 3)unlike adults, all infants lacked frontal alpha predominance and coherence. Alpha power was greatest during maintenance, compared to awake and emergence in infants at 4-6months. During emergence, theta and alpha power decreased with decreasing sevoflurane concentration in infants at 4-6months. These EEG dynamic differences are likely due to developmental factors including regional differences in synaptogenesis, glucose metabolism, and myelination across the cortex. We demonstrate the need to apply age-adjusted analytic approaches to develop neurophysiologic-based strategies for pediatric anesthetic state monitoring.
    eLife Sciences 06/2015; 4. DOI:10.7554/eLife.06513
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    ABSTRACT: Classical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series. This universally accepted approach fails to exploit the temporal continuity in the data and is not well-suited for signals with highly structured time–frequency representations. For a time series whose time-varying mean is the superposition of a small number of oscillatory components, we formulate nonparametric batch spectral analysis as a Bayesian estimation problem. We introduce prior distributions on the time–frequency plane that yield maximum a posteriori (MAP) spectral estimates that are continuous in time yet sparse in frequency. Our spectral decomposition procedure, termed spectrotemporal pursuit, can be efficiently computed using an iteratively reweighted least-squares algorithm and scales well with typical data lengths. We show that spectrotemporal pursuit works by applying to the time series a set of data-derived filters. Using a link between Gaussian mixture models, ℓ[subscript 1] minimization, and the expectation–maximization algorithm, we prove that spectrotemporal pursuit converges to the global MAP estimate. We illustrate our technique on simulated and real human EEG data as well as on human neural spiking activity recorded during loss of consciousness induced by the anesthetic propofol. For the EEG data, our technique yields significantly denoised spectral estimates that have significantly higher time and frequency resolution than multitaper spectral estimates. For the neural spiking data, we obtain a new spectral representation of neuronal firing rates. Spectrotemporal pursuit offers a robust spectral decomposition framework that is a principled alternative to existing methods for decomposing time series into a small number of smooth oscillatory components.
    Proceedings of the National Academy of Sciences 06/2015; 111(50). DOI:10.1073/pnas.1320637111
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    ABSTRACT: Switching from maintenance of general anesthesia with an ether anesthetic to maintenance with high-dose (concentration >50% and total gas flow rate >4liters per minute) nitrous oxide is a common practice used to facilitate emergence from general anesthesia. The transition from the ether anesthetic to nitrous oxide is associated with a switch in the putative mechanisms and sites of anesthetic action. We investigated whether there is an electroencephalogram (EEG) marker of this transition. We retrospectively studied the ether anesthetic to nitrous oxide transition in 19 patients with EEG monitoring receiving general anesthesia using the ether anesthetic sevoflurane combined with oxygen and air. Following the transition to nitrous oxide, the alpha (8-12Hz) oscillations associated with sevoflurane dissipated within 3-12min (median 6min) and were replaced by highly coherent large-amplitude slow-delta (0.1-4Hz) oscillations that persisted for 2-12min (median 3min). Administration of high-dose nitrous oxide is associated with transient, large amplitude slow-delta oscillations. We postulate that these slow-delta oscillations may result from nitrous oxide-induced blockade of major excitatory inputs (NMDA glutamate projections) from the brainstem (parabrachial nucleus and medial pontine reticular formation) to the thalamus and cortex. This EEG signature of high-dose nitrous oxide may offer new insights into brain states during general anesthesia. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
    Clinical neurophysiology: official journal of the International Federation of Clinical Neurophysiology 06/2015; 121. DOI:10.1016/j.clinph.2015.06.001
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    ABSTRACT: Medical coma is an anesthetic-induced state of brain inactivation, manifest in the electroencephalogram by burst suppression. Feedback control can be used to regulate burst suppression, however, previous designs have not been robust. Robust control design is critical under real-world operating conditions, subject to substantial pharmacokinetic and pharmacodynamic parameter uncertainty and unpredictable external disturbances. We sought to develop a robust closed-loop anesthesia delivery (CLAD) system to control medical coma. We developed a robust CLAD system to control the burst suppression probability (BSP). We developed a novel BSP tracking algorithm based on realistic models of propofol pharmacokinetics and pharmacodynamics. We also developed a practical method for estimating patient-specific pharmacodynamics parameters. Finally, we synthesized a robust proportional integral controller. Using a factorial design spanning patient age, mass, height, and gender, we tested whether the system performed within clinically acceptable limits. Throughout all experiments we subjected the system to disturbances, simulating treatment of refractory status epilepticus in a real-world intensive care unit environment. In 5400 simulations, CLAD behavior remained within specifications. Transient behavior after a step in target BSP from 0.2 to 0.8 exhibited a rise time (the median (min, max)) of 1.4 [1.1, 1.9] min; settling time, 7.8 [4.2, 9.0] min; and percent overshoot of 9.6 [2.3, 10.8]%. Under steady state conditions the CLAD system exhibited a median error of 0.1 [-0.5, 0.9]%; inaccuracy of 1.8 [0.9, 3.4]%; oscillation index of 1.8 [0.9, 3.4]%; and maximum instantaneous propofol dose of 4.3 [2.1, 10.5] mg kg(-1). The maximum hourly propofol dose was 4.3 [2.1, 10.3] mg kg(-1) h(-1). Performance fell within clinically acceptable limits for all measures. A CLAD system designed using robust control theory achieves clinically acceptable performance in the presence of realistic unmodeled disturbances and in spite of realistic model uncertainty, while maintaining infusion rates within acceptable safety limits.
    Journal of Neural Engineering 05/2015; 12(4):046004. DOI:10.1088/1741-2560/12/4/046004
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    ABSTRACT: We consider the problem of recovering a sequence of vectors, (Xk)[K over k=0], for which the increments X[subscript k] - X[subscript k-1] are S[subscript k]-sparse (with S[subscript k] typically smaller than S[subscript 1]), based on linear measurements (Y[subscript k] = A[subscript k]X[subscript k] + e[subscript k)[superscript K over k=1, where A[subscript k] and e[subscript k] denote the measurement matrix and noise, respectively. Assuming each A[subscript k] obeys the restricted isometry property (RIP) of a certain order--depending only on S[subscript k]--we show that in the absence of noise a convex program, which minimizes the weighted sum of the ℓ [subscript 1]-norm of successive differences subject to the linear measurement constraints, recovers the sequence (Xk)[K over k=1] exactly. This is an interesting result because this convex program is equivalent to a standard compressive sensing problem with a highly-structured aggregate measurement matrix which does not satisfy the RIP requirements in the standard sense, and yet we can achieve exact recovery. In the presence of bounded noise, we propose a quadratically-constrained convex program for recovery and derive bounds on the reconstruction error of the sequence. We supplement our theoretical analysis with simulations and an application to real video data. These further support the validity of the proposed approach for acquisition and recovery of signals with time-varying sparsity.
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    ABSTRACT: Deep hypothermia induces ‘burst suppression’ (BS), an electroencephalogram pattern with low-voltage ‘suppressions’ alternating with high-voltage ‘bursts’. Current understanding of BS comes mainly from anesthesia studies, while hypothermia-induced BS has received little study. We set out to investigate the electroencephalogram changes induced by cooling the human brain through increasing depths of BS through isoelectricity.
    Clinical Neurophysiology 01/2015; DOI:10.1016/j.clinph.2014.12.022
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    ABSTRACT: Anesthesia-induced altered arousal depends on drugs having their effect in specific brain regions. These effects are also reflected in autonomic nervous system (ANS) outflow dynamics. To this extent, instantaneous monitoring of ANS outflow, based on neurophysiological and computational modeling, may provide a more accurate assessment of the action of anesthetic agents on the cardiovascular system. This will aid anesthesia care providers in maintaining homeostatic equilibrium and help to minimize drug administration while maintaining antinociceptive effects. In previous studies, we established a point process paradigm for analyzing heartbeat dynamics and have successfully applied these methods to a wide range of cardiovascular data and protocols. We recently devised a novel instantaneous nonlinear assessment of ANS outflow, also suitable and effective for real-time monitoring of the fast hemodynamic and autonomic effects during induction and emergence from anesthesia. Our goal is to demonstrate that our framework is suitable for instantaneous monitoring of the ANS response during administration of a broad range of anesthetic drugs. Specifically, we compare the hemodynamic and autonomic effects in study participants undergoing propofol (PROP) and dexmedetomidine (DMED) administration. Our methods provide an instantaneous characterization of autonomic state at different stages of sedation and anesthesia by tracking autonomic dynamics at very high time-resolution. Our results suggest that refined methods for analyzing linear and nonlinear heartbeat dynamics during administration of specific anesthetic drugs are able to overcome nonstationary limitations as well as reducing inter-subject variability, thus providing a potential real-time monitoring approach for patients receiving anesthesia.
    12/2014; 1(1). DOI:10.1186/s40244-014-0013-2
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    ABSTRACT: eLife digest Although we are all familiar with the experience of being conscious, explaining precisely what consciousness is and how it arises from activity in the brain remains extremely challenging. Indeed, explaining consciousness is so challenging that it is sometimes referred to as ‘the hard question’ of neuroscience. One way to obtain insights into the neural basis of consciousness is to compare patterns of activity in the brains of conscious subjects with patterns of brain activity in the same subjects under anesthesia. The results of some experiments of this kind suggest that loss of consciousness occurs when the communication between specific regions within the outer layer of the brain, the cortex, is disrupted. However, other studies seem to contradict these findings by showing that this communication can sometimes remain intact in unconscious subjects. Akeju, Loggia et al. have now resolved this issue by using brain imaging to examine the changes that occur as healthy volunteers enter and emerge from a light form of anesthesia roughly equivalent to non-REM sleep. An imaging technique called PET revealed that the loss of consciousness in the subjects was accompanied by reduced activity in a structure deep within the brain called the thalamus. Reduced activity was also seen in areas of cortex at the front and back of the brain. A technique called fMRI showed in turn that communication between the cortex and the thalamus was disrupted as subjects drifted into unconsciousness, whereas communication between cortical regions was spared. As subjects awakened from the anesthesia, communication between the thalamus and the cortex was restored. These results suggest that changes within distinct brain regions give rise to different depths of unconsciousness. Loss of communication between the thalamus and the cortex generates the unconsciousness of sleep or light anesthesia, while the additional loss of communication between cortical regions generates the unconsciousness of general anesthesia or coma. In addition to explaining the mixed results seen in previous experiments, this distinction could lead to advances in the diagnosis of patients with disorders of consciousness, and even to the development of therapies that target the thalamus and its connections with cortex. DOI: http://dx.doi.org/10.7554/eLife.04499.002
    eLife Sciences 11/2014; 4. DOI:10.7554/eLife.04499
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    ABSTRACT: The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.
    PLoS Computational Biology 10/2014; 10(10):e1003866. DOI:10.1371/journal.pcbi.1003866
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    ABSTRACT: The neural mechanisms of anesthetic vapors have not been studied in depth. However, modeling and experimental studies on the intravenous anesthetic propofol indicate that potentiation of γ-aminobutyric acid receptors leads to a state of thalamocortical synchrony, observed as coherent frontal alpha oscillations, associated with unconsciousness. Sevoflurane, an ether derivative, also potentiates γ-aminobutyric acid receptors. However, in humans, sevoflurane-induced coherent frontal alpha oscillations have not been well detailed.
    Anesthesiology 09/2014; 121(5). DOI:10.1097/ALN.0000000000000436
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    ABSTRACT: Background: Electroencephalogram patterns observed during sedation with dexmedetomidine appear similar to those observed during general anesthesia with propofol. This is evident with the occurrence of slow (0.1 to 1 Hz), delta (1 to 4 Hz), propofol-induced alpha (8 to 12 Hz), and dexmedetomidine-induced spindle (12 to 16 Hz) oscillations. However, these drugs have different molecular mechanisms and behavioral properties and are likely accompanied by distinguishing neural circuit dynamics. Methods: The authors measured 64-channel electroencephalogram under dexmedetomidine (n = 9) and propofol (n = 8) in healthy volunteers, 18 to 36 yr of age. The authors administered dexmedetomidine with a 1-mu g/kg loading bolus over 10 min, followed by a 0.7 mu g kg(-1) h(-1) infusion. For propofol, the authors used a computer-controlled infusion to target the effect-site concentration gradually from 0 to 5 g/ml. Volunteers listened to auditory stimuli and responded by button press to determine unconsciousness. The authors analyzed the electroencephalogram using multitaper spectral and coherence analysis. Results: Dexmedetomidine was characterized by spindles with maximum power and coherence at approximately 13 Hz (mean SD; power, -10.8 +/- 3.6 dB; coherence, 0.8 +/- 0.08), whereas propofol was characterized with frontal alpha oscillations with peak frequency at approximately 11 Hz (power, 1.1 +/- 4.5 dB; coherence, 0.9 +/- 0.05). Notably, slow oscillation power during a general anesthetic state under propofol (power, 13.2 +/- 2.4 dB) was much larger than during sedative states under both propofol (power, -2.5 +/- 3.5 dB) and dexmedetomidine (power, -0.4 +/- 3.1 dB). Conclusion: The results indicate that dexmedetomidine and propofol place patients into different brain states and suggest that propofol enables a deeper state of unconsciousness by inducing large-amplitude slow oscillations that produce prolonged states of neuronal silence.
    Anesthesiology 09/2014; 121(5). DOI:10.1097/ALN.0000000000000419
  • Behtash Babadi, Emery N. Brown, Demba E. Ba, Patrick Lee Purdon
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    ABSTRACT: In this paper, we study the theoretical properties of iteratively re-weighted least squares (IRLS) algorithms and their utility in sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between the IRLS algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribution. The EM formalism, as well as the connection to GSMs, allow us to establish that the IRLS algorithms minimize smooth versions of the lν `norms', for . We leverage EM theory to show that the limit points of the sequence of IRLS iterates are stationary points of the smooth lν “norm” minimization problem on the constraint set. We employ techniques from Compressive Sampling (CS) theory to show that the IRLS algorithm is stable, if the limit point of the iterates coincides with the global minimizer. We further characterize the convergence rate of the IRLS algorithm, which implies global linear convergence for ν = 1 and local super-linear convergence for . We demonstrate our results via simulation experiments. The simplicity of IRLS, along with the theoretical guarantees provided in this contribution, make a compelling case for its adoption as a standard tool for sparse signal recovery.
  • Emery N. Brown, Patrick Lee Purdon, Christa Van Dort
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    ABSTRACT: Placing a patient in a state of general anesthesia is crucial for safely and humanely performing most surgical and many nonsurgical procedures. How anesthetic drugs create the state of general anesthesia is considered a major mystery of modern medicine. Unconsciousness, induced by altered arousal and/or cognition, is perhaps the most fascinating behavioral state of general anesthesia. We perform a systems neuroscience analysis of the altered arousal states induced by five classes of intravenous anesthetics by relating their behavioral and physiological features to the molecular targets and neural circuits at which these drugs are purported to act. The altered states of arousal are sedation-unconsciousness, sedation-analgesia, dissociative anesthesia, pharmacologic non-REM sleep, and neuroleptic anesthesia. Each altered arousal state results from the anesthetic drugs acting at multiple targets in the central nervous system. Our analysis shows that general anesthesia is less mysterious than currently believed.
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    ABSTRACT: (Background) Accurate quantitative analysis of the changes in responses to external stimuli is crucial for characterizing the timing of loss and recovery of consciousness induced by anesthetic drugs. We studied induction and emergence from unconsciousness achieved by administering a computer-controlled infusion of propofol to ten human volunteers. We evaluated loss and recovery of consciousness by having subjects execute every four seconds two interleaved computer delivered behavioral tasks: responding to verbal stimuli (neutral words or the subject's name), or less salient stimuli of auditory clicks. (New Method) We analyzed the data using state-space methods. For each stimulus type the observation model is a two-stage binomial model and the state model is two dimensional random walk in which one cognitive state governs the probability of responding and the second governs the probability of correctly responding given a response. We fit the model to the experimental data using Bayesian Monte Carlo methods. (Results) During induction subjects lost responsiveness to less salient clicks before losing responsiveness to the more salient verbal stimuli. During emergence subjects regained responsiveness to the more salient verbal stimuli before regaining responsiveness to the less salient clicks. (Comparison with Existing Method(s)) The current state-space model is an extension of previous model used to analyze learning and behavioral performance. In this study, the probability of responding on each trial is obtained separately from the probability of behavioral performance. (Conclusions) Our analysis provides a principled quantitative approach for defining loss and recovery of consciousness in experimental studies of general anesthesia.
    Journal of neuroscience methods 04/2014; 227. DOI:10.1016/j.jneumeth.2014.01.026
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    ABSTRACT: Rhythmic oscillations shape cortical dynamics during active behavior, sleep, and general anesthesia. Cross-frequency phase-amplitude coupling is a prominent feature of cortical oscillations, but its role in organizing conscious and unconscious brain states is poorly understood. Using high-density EEG and intracranial electrocorticography during gradual induction of propofol general anesthesia in humans, we discovered a rapid drug-induced transition between distinct states with opposite phase-amplitude coupling and different cortical source distributions. One state occurs during unconsciousness and may be similar to sleep slow oscillations. A second state occurs at the loss or recovery of consciousness and resembles an enhanced slow cortical potential. These results provide objective electrophysiological landmarks of distinct unconscious brain states, and could be used to help improve EEG-based monitoring for general anesthesia.
    The Journal of Neuroscience : The Official Journal of the Society for Neuroscience 01/2014; 34(3):839-45. DOI:10.1523/JNEUROSCI.5813-12.2014
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    ABSTRACT: In this paper, we study the theoretical properties of iteratively re-weighted least squares (IRLS) algorithms and their utility in sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between the IRLS algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribution. The EM formalism, as well as the connection to GSMs, allow us to establish that the IRLS algorithms minimize smooth versions of the $ell_{nu}$ ‘norms’, for $0 < nu leq 1$. We leverage EM theory to show that the limit points of the sequence of IRLS iterates are stationary points of the smooth $ell_{nu}$ “norm” minimization problem on the constraint set. We employ techniques from Compressive Sampling (CS) theory to show that the IRLS algorithm is stable, if the limit point of the iterates coincides with the global minimizer. We further characterize the convergence rate of the IRLS algorithm, which implies global linear convergence for $nu =1$ and local super-linear convergence for $0< nu < 1$. We demonstrate our results via simulation experiments. The simplicity of IRLS, along with the theoretical guarantees provided in this contribution, make a compelling case for its adoption as a standard tool for sparse signal recovery.
    IEEE Transactions on Signal Processing 01/2014; 62(1):183-195. DOI:10.1109/TSP.2013.2287685

Publication Stats

1k Citations
308.80 Total Impact Points

Institutions

  • 2006–2015
    • Harvard Medical School
      • • Department of Anesthesia
      • • Athinoula A. Martinos Center for Biomedical Imaging
      Boston, Massachusetts, United States
  • 2001–2015
    • Massachusetts General Hospital
      • • Department of Anesthesia, Critical Care and Pain Medicine
      • • Diabetes Clinical Research Center
      • • Athinoula A. Martinos Center for Biomedical Imaging
      Boston, Massachusetts, United States
    • University of New South Wales
      • School of Electrical Engineering and Telecommunications
      Kensington, New South Wales, Australia
  • 2009–2014
    • Harvard University
      • Center for Brain Science
      Cambridge, Massachusetts, United States
  • 2007–2013
    • Massachusetts Institute of Technology
      • Department of Brain and Cognitive Sciences
      Cambridge, Massachusetts, United States
  • 2011
    • Imperial College London
      Londinium, England, United Kingdom